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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 4, Pages 729-734
http://dx.doi.org/10.1155/S016117129800101X

Atomoicity of mappings

1Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, Wrocław 50-384, Poland
2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México 04510, D.F., Mexico
3Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México 04510, D.F., Mexico

Received 16 December 1996; Revised 11 December 1997

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A mapping f:XY between continua X and Y is said to be atomic at a subcontinuumK of the domain X provided that f(K) is nondegenerate and K=f1(f(K)). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of X, is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.